The present invention is derived from a striking novel discovery, that porous crystalline materials have piezoelectric and piezooptic properties. The present invention, therefore, relates to devices and methods which take advantage of this newly discovered phenomenon. One main use of this discovery is in the field of adaptive optics, e.g., adaptive reflectors such as mirrors, however, other uses, as is further delineated below, are anticipated. Thus, for example, the new technology can find uses in (i) attached fiber optics maneuvering (movement of fiber for focusing etc.); (ii) attached fiber optic bending for mode control; (iii) attached fiber optics intensity and polarization control; (iv) spatial light modulation (electro optical and opto-optical modulation) by adjustment of specific elements or a whole device; (v) tunneling devices, where the tunneling current is sensitive to distance between elements; (vi) scanning microscopy heads, optical or magnetic disc readers which have to be maneuvered by electric or light signal; and (vii) light or voltage detectors.
Most of the following background discussion, however, focuses on the construction, fabrication, use, advantages and limitations of prior art adaptive mirrors, however, there is no intention to restrict the use of the newly discovered piezoelectric and piezooptic properties of porous crystalline materials to the field of adaptive optics, as many other uses and applications of this core technology are envisaged.
Adaptive optics systems are essentially a servo loop, with a sensitive wave front sensor, a control computer, and a flexible mirror to correct aberrations in a beam of light. Despite large efforts made in the last few decades, progress in deformable mirrors has been slow, and there are only a few kinds available. The high price of these mirrors is an indicator of the problems in their manufacture, such as complex construction, non-repeatability and non-uniformity.
What is required of an adaptive mirror? It has to be agile enough to correct even the strongest and densest wave front fluctuations (usually a few micrometers in stroke), while not contributing errors of its own. The more elements it has the better, ranging between few and thousands of actuators. It has to be quick enough to correct even the fastest variations, while not resonating close to the operational frequency. It has to run on low power to avoid a cumbersome power supply and control system, while not loosing in dynamic range. It has to be small and light enough to mount in a compact space. It has to be fail-safe or at least allow easy correction or replacement of bad elements. It has to have serial command lines to the elements to avoid massively parallel wiring. Mechanically, it needs to be of good optical quality and insensitive to temperature variations, even without active correction. Finally, it ought to have a sound price, which is derived mainly from its construction technology.
There are many other fields where actuation of devices is a part of their operation: communication devices, switching devices, scanning microscopes, printers, and many more depend on mechanical movement of smaller or larger parts as a response to an electronic or optical command. The discussion below will concentrate on adaptive optics (or the slower active optics) as a relevant example: such systems change the path of light beams, their direction or the wave front emanating from them, usually to correct aberrations.
Lets start with the simpler systems, those that can serve as basis for systems that are more complex. Lets define these systems as being able to correct only one mode at a time. The lowest modes would be those which can be defined by one parameter over the correction area. Zernike decomposition, which is common for optical round apertures, has basic modes as follows: (i) piston correction (given value of the wave front), this mode is important only when using a segmented mirror; (ii) tip and tilt (given value of the wave front derivatives in x and y directions; and (iii) defocus (given value of the wave front curvature).
Piston correction is achieved merely by moving the mirror surface up and down, while maintaining its direction. The size of the elements d is small compared to the lateral scale of the aberrations. Mirror movement in parallel to itself is achieved by piston actuators; these actuators are the basis of most deformable mirrors. Mentioned here are some commonly used devices. Comparative designs and analyses have appeared in J. A. Pearson, R. H. Freeman, and Harold C. Reynolds, Jr., ‘Adaptive optical techniques for wave-front correction’, in Applied Optics and Optical Engineering Vol. VII, R. R. Shannon and. C. Wyant, editors, Academic Press, 246-340, 1979; M. A. Ealey, ‘Actuators: design fundamentals, key performance specifications, and parametric trades’, SPIE Vol. 1543, 346-362, 1991; M. A. Ealey and J. A. Wellman, ‘Deformable mirrors: design fundamentals, key performance specifications, and parametric trades’, SPIE 1543, 36-51, 1991; E. N. Ribak, ‘Deformable mirrors’, in Adaptive Optics in Astronomy, NATO ASI Vol. 423, 149-62, 1994; R. K. Tyson, Principles of Adaptive Optics, Academic Press, 1998; R. E. Aldrich, ‘Deformable mirror wavefront correctors’, in Adaptive Optics Engineering Handbook, Marcel Dekker, 2000. The main types of deformable mirrors appear in FIGS. 1a-f, each of which has its limitations.
The most common method of piston correction is by using piezoelectric actuators. These actuators are very convenient since they respond directly and quite linearly to an applied voltage. Their response (for lead zirconium titanate, the most common material) is in the order of 1 micrometer for 1 kV, which is too small to achieve the several microns required to correct for atmospheric turbulence. Only one mirror was used in this configuration: the monolithic piezoelectric mirror [J. S. Feinlieb, S. G. Lipson, and P. E. Cone, ‘Monolithic piezoelectric for wavefront correction’, Appl. Phys. Lett. Vol. 25, 311-315, 1974], where the electrode contacts were drilled through the actuator block almost to the face of the mirror. A number of schemes were devised for better voltage response. In one scheme use is made of the thickness-to-length ratio: instead of applying the voltage along the most responsive direction, it is applied across this direction. By making the piezoelectric material very long and very thin, the transverse response is amplified by this ratio. Since they are constructed from ceramic materials, these actuators can be manufactured in almost any desired shape. For this application they are prepared in a tubular shape, which is convenient for other applications. Another choice is to bond a stack of many thin slabs of the material, and apply low voltage on all of them in cascade. The slabs are combined with their polarizations directions alternating so that application of the voltage is in parallel.
Another piezoelectric material is lead magnesium niobate, with a better (but uni-directional) voltage response and lower hysteresis [G. H. Blackwood, P. A. Davis, and M. A. Ealey, ‘Characterization of MMN:BA electrostrictive plates and SELECT actuators at low temperatures’, SPIE Vol. 1543, 422-429, [Blackwood et al., 1991]. This kind of response is called electrostrictive. However, since it always extends, either under positive or negative voltage, a bias voltage must be applied to it for bi-directional movement.
Another option for actuators is the voice coil, such as used in commercial loud speakers. In this case, a magnetic field drives a coil attached to a piston. The drawback here is the heating created by the flowing current. The magnetostrictive actuator consists of a solenoid within which is the magnetostrictive ferrite whose length changes under magnetic field. Here again the actuator has to be rid of the heat in the solenoid. It is easier to use these actuators in a laser adaptive mirror, since both have to be cooled anyway.
The hydraulic actuator is able to provide force by amplification of mechanical force or by employing a valve to control a constant high pressure. Severe drawbacks such as requirements for both a hydraulic system and an electrical one, slow response and large volume make them less convenient to employ.
Finally, electrostatic actuation is used for membrane mirrors, and is discussed further below. A full comparison between the different actuators can be found in the general references cited above.
Tip and tilt correction should be separated from the case of a steering correction. Tip and tilt are required in multi-element systems, where the wave front will not be continuous between actuators. To minimize this effect the tip and tilt are supplemented by piston movement.
A steering mirror only corrects the direction of the incoming beam. It is utilized for telescopes which cannot track in a smooth manner or for initial correction for turbulence-induced wave front tilts. In this capacity it is also employed sometimes as the first stage in an adaptive optics system to reduce requirements on the main deformable mirror. A full list of design parameters for such mirrors can be found in [L. M. Germann, ‘Specifications of fine-steering mirrors for line-of-sight stabilization systems’, SPIE Vol. 1543, 202-212, 1991].
Steering mirrors have two degrees of freedom, whereas tip-tilt correctors require three. All designs on the market today utilize pistons to push and pull on the back of a high quality mirror. Some of the mirrors are metallic (molybdenum or beryllium) for power applications and for high speed response. The requirement to maintain a flat surface is alleviated if steering mirrors are used as a first stage before a deformable mirror, since a servo loop could correct for the residual errors.
Steering and tip/tilt/piston mirrors can have a number of mechanical designs. One design uses direct piezoelectric actuators or lever-amplified ones. In another design use is made of tubular piezoelectric material. Sectors along the tube are powered separately to both bend and piston the supported mirror. There are also voice coil pistons and electromagnetic pistons. The number of actuators varies between two and four, depending on the specific application.
Defocus can be corrected by a mirror whose radius of curvature can be controlled. This mode of operation can be achieved in the bimorph mirror. In this device, the actuator is not pushing against the back of the mirror or pulling it down, but acts to stretch along the surface of the mirror. In a construction similar to the bimetallic strip, a thin actuator is glued to the surface of a thin mirror. When voltage is applied to it, it expands in area (when thin enough, the lateral contraction is negligible). In a manner similar to the bimetallic strip under heating, this expansion, combined with the inert mirror, leads to the structure curving. Another possibility is to have the actuators glued back to back so that the bending is doubled. In this case they have to be polished properly to optical quality. It can be shown [Steinhaus E., and S. G. Lipson, ‘Bimorph piezoelectric flexible mirror’, J. Opt. Soc. Am. Vol. 69, 478-481, 1979] that the curvature of the surface is proportional to the applied voltage.
Another way to achieve a spherical surface is by electrostatic pull. A thin conducting membrane is pulled towards a plane and (initially) parallel electrode which is charged to create a capacitor. The amount of charge sets the amount of curvature. A transparent electrode is sometimes required to pull on the membrane in the opposite direction and to protect it from acoustic noise sources [F. Merkle, K. Freischlad, J. Bille, ‘Development of an active optical mirror for astronomical applications’, ESO Conference on Scientific Importance of High Angular Resolution at Infrared and Optical Wavelengths, 41-44, 1981, M. Clampin, S. T. Durrance, D. A. Golimowski, and R. H. Barkhouser, ‘The Johns Hopkins adaptive optics coronograph’, SPIE Vol. 1542, 165-74, 1991, G. Vdovin, ‘Micromachined membrane deformable mirror’, in Adaptive Optics Engineering Handbook, Rk. Tyson, Rd., Marcel Dekker 2000].
So far the discussion was focused on segmented mirrors which are simpler to construct and maintain, easily understood, and straightforward to run. Unfortunately, they cannot mimic the aberrated wave front too well, and they have gaps between the mirrors.
These drawbacks do not exist for the competition: continuous mirrors. Here the front surface consists of a single unit, usually called the face plate or face sheet, and it is acted upon from behind by actuators of various sorts. The actuators separate into two kinds: piston actuators, which act on the face sheet normal to its surface, and bending actuators, which act in parallel to the surface.
Piston actuation: Applying a force normal to the surface requires a special attachment of the actuator to the face plate. The actuator has to push and pull on the surface using some heavy and solid back reference plane. The attachments of the actuator to the base and to the mirror have some special—and sometimes conflicting—requirements:                1. Yield or backlash below the required wave front accuracy (usually below 0.1 micrometer in the normal direction, 0.5 micrometer inside the plane of the face sheet).        2. Possibility for simple and accurate replacement of a faulty actuator (this is especially important for multiple element mirrors).        3. Foot-print (projected area of the actuator on the mirror) allowing high density of elements. The base attachment foot-print also has to allow power lines to the actuator.        4. Print-through (induced local mirror aberration) at the required wave front accuracy (say 0.1 micrometer) at all lateral scales which cannot be corrected by the actuators themselves.        5. Adjustment for zero power: means to set the mirror surface flat if the actuators are not powered (the telescope must still function when the deformable mirror is turned off). In some cases this adjustment can be achieved by a constant bias on the elements, which reduces the dynamic range of the actuators. In these cases the zero adjustment can be coarser and only place the actuator in its application margin.        6. Preloading of the actuators is sometimes required. Piezoelectric actuators, for example, function better against pressure.        7. The three-dimensional shape of the attachment is extremely important for tailoring an appropriate influence function.        8. The frequency response of the structure has to be as linear as possible, and the first resonance frequency high above the atmospheric fastest fluctuations.        
A common attachment between actuator and face plate is magnetic. A thin ferromagnetic plate is glued to the back of the face plate. Permanent magnets are used to attach the actuators to it. Another choice is to glue an end piece to the mirror and to attach the actuator to it. In less expensive mirrors the actuator is glued directly to the face plate.
Influence functions: When an actuator pushes or pulls on a mirror, the surface of the mirror attains a hill or a valley shape centered around the attachment point. This shape is called the actuator influence function, although analytic functions do not describe it too well. It depends on the following parameters:                1. Face plate material properties.        2. Actuator attachment geometry and material.        3. Location of neighboring actuators. The distance to the neighbors, their arrangement (square or hexagonal), and even the non-existence of neighbors near the border all affect the influence function.        4. Repeatability of the response of the actuators and their attachments.        
The importance of the influence function is in the calculation of the fit of the mirror to the wave front. If each actuator has a three dimensional influence function of its own, than the control computer must perform a very large and time consuming fit of the whole wave front to the whole mirror. Even influence functions whose size is larger than the actuator-to-actuator distance complicate this calculation. Thus, having a constant and repeatable influence function which can be tabulated or modeled by a simple function (e.g., cubic spline, gaussian, cosine) is extremely important. This difficult point was realized and tackled from very early on [see the general references and H. R. Hiddleston, D. David Lyman, and E. L. Schafer, ‘Comparisons of deformable mirror models and influence functions’, SPIE Vol. 1542, 20-34, 1991]. The problem is much easier for membrane mirrors. The use of faster and larger computers has somewhat reduced the need for a stationary influence function.
Membrane mirrors: Membrane mirrors are those whose face plate is relatively thin. Deformable mirrors which use piston actuation tend to have thicker face plate, since the available force is usually much more than required (although the stroke might be limited). In two cases there is an advantage to thinner surfaces. Both cases allow longer strokes, but are limited in force and have rather high acoustic pick-up. The first case is the electrostatic membrane mirror, which belongs in the piston actuators, and the second is the bimorph mirror, which utilizes bending of the membrane surface.
The electrostatic membrane deformable mirror is essentially made of a set of capacitors which are laid in parallel, both physically and electrically. The membrane is made of a conducting, reflective material of limited thickness (a few microns). This device is the extension of a single such mirror. The electrostatic pull between the surfaces of the capacitor is uni-directional, and it is required to devise some scheme to have a two-directional motion. One way is to bias all the elements at some high voltage, and have all elements move in a small range above and below this bias. This electric bias creates a spherical bias surface which has to be included in the design of the optical system. A way to avoid bias is to put an opposite electrode on the other side of the membrane to pull in the other direction. This electrode is transparent and allows the enclosure of the whole device.
The voltages required to achieve the desired stroke depend on the spacing between the membrane and the opposite electrodes, and range between few volts to hundreds of volts. This spacing cannot be made too small so as to avoid the membrane short-circuiting to the electrodes, and also to allow some air to remain and dampen vibrations of the membrane. Too tight a space is also a problem since the air has no room to escape when the membrane moves. The small room between the electrodes and the membrane require very accurate machining of the electrodes to avoid edge effects (sharp edges have a higher electrostatic field). A biased membrane will require a curved electrode surface to best match its equilibrium position. Finally, the membrane tends to vibrate very easily, so it needs an efficient damping mechanism (such as air) to be included in the design.
Bimorph mirrors: Bimorph mirrors depend on membrane face sheets for flexibility. They are constructed of a thin piezoelectric material bonded to a thin mirror. The curvature depends on the square of ratio of the diameter to the thickness, which explains why they come under the heading of membranes. There are a number of ways to have a multiple electrode bimorph mirror. The first is to have a large piezoelectric sheet attached to a large face sheet. The electrodes are drawn on the back of the piezoelectric sheet in any desired shape [F. Forbes and N. Roddier, ‘Adaptive optics using curvature sensing’, in SPIE Vol. 1542, 140-147, 1991]. This method is limited due to the fragile nature of the ceramic piezoelectric material that does not allow two high a ratio of the diameter to the thickness.
A second method is to glue many electrodes to the back of a single face sheet [E. N. Ribak, S. G. Lipson, and C. Schwartz, ‘Thin mirror adaptation by simulated annealing’, ESO Conference on high-resolution imaging by interferometry II, 1991, ‘High performance, affordable agile mirror’, Air Force workshop on Declassification of Military Technology: Laser Guide Stars, Albuquerque, N. Mex., 1992]. This allows for the same piezoelectric material thickness to effectively increase the size of the device. The draw-back is that a very thin face sheet is sensitive to print-through effects caused by edges of the piezoelectric elements. Glue expansion at the elements edges is a severe problem, which can only be resolved by using thicker face sheet and reducing the voltage sensitivity [C. Schwartz, E. Ribak, and S. G. Lipson, ‘Bimorph adaptive mirrors and curvature sensing’, J. Opt. Soc. Am. A Vol. 11, 895-902, 1994]. A stroke of one wave length requires between seven and twenty volts, depending on the dimensions of the bimorph.
A significant difference between piston mirrors and membrane mirrors is their voltage response. Each actuator has a spatial response which is linear with its displacement and extends to approximately the next element. Bimorph mirrors can be shown to solve the bi-harmonic equation, or, under simplifying assumptions, the Poisson equation [Steinhaus E., and S. G. Lipson, ‘Bimorph piezoelectric flexible mirror’, J. Opt. Soc. Am. Vol. 69, 478-481, 1979; C. Schwartz, E. Ribak, and S. G. Lipson, ‘Bimorph adaptive mirrors and curvature sensing’, J. Opt. Soc. Am. A Vol. 11, 895-902, 1994]. This means that the surface curvature is linear with the voltage distribution, and that this response extends to neighboring elements.
Because curvature is induced, not displacement, the membrane mirror is easier to control using most wave front sensors. Essentially all such sensors measure either the wave front first derivative (Hartmann-Shack sensors, shearing interferometers) or the second derivative (curvature sensors). In order to calculate displacement, it is necessary to integrate the gradient or laplacian measurements once or twice. Differentiating the gradient or directly applying the curvature to the membrane is much simpler [F. Forbes and N. Roddier, ‘Adaptive optics using curvature sensing’, in SPIE Vol. 1542, 140-147, 1991; C. Schwartz, E. Ribak, and S. G. Lipson, ‘Bimorph adaptive mirrors and curvature sensing’, J. Opt. Soc. Am. A Vol. 11, 895-902, 1994]. Some modification might be needed because the coupling between the curvature sensor and the bimorph mirror has to take into account coupling between correction terms and edge effects.
Addition of tip/tilt correction: The most severe aberration of the wave front is due to very large scale fluctuations. Since the dynamic range of the stroke of most piston mirrors is quite limited, this low order aberration is often taken care of separately by a steering mirror. The main deformable mirror corrects only residual errors of higher frequency. The situation is better for bimorph mirrors, since their stroke is usually longer. In addition, correction of the lower Fourier components can be achieved on the border and outside the active mirror surface, with virtually no effect on the rest of the elements. This is because the voltage sets the bimorph curvature, and this curvature is independent of the large scale tilt.
Various other devices were proposed for deformable mirrors. Spatial light modulators, useful for image processing, are usually limited by spectral, spatial and temporal band-width. Oil films whose thickness can be varied electrostatically were also proposed in the past, but rejected for the same reasons. Two more options are the utilization of laser corrective mirrors and of liquid crystal modulators.
Corrective laser mirrors: Devices built for correction of laser mode hopping and for transmission of laser beams through turbulence can also serve for astronomical applications. These mirrors are manufactured to tolerate very high intensities, and the mirrors for atmospheric correction also respond at high enough frequency. The face plates are usually metallic (e.g., beryllium, molybdenum) for good thermal conductivity. The structure includes means for liquid cooling of the front surface and sometimes of the actuators. Unfortunately, these qualities make the mirrors extremely complex to construct, maintain, and run.
Liquid crystals: Liquid crystals were proposed for wave front correctors. The mechanism is electro-optical path correction by modulation of nematic liquid crystals. An addressable matrix has the refractive index change by as much as 0.2 on a scale of 10 micrometers. Light reflected through the liquid crystal has its optical path changed at the rate of more than 1 micrometer in 50 ms, which is adequate. A very large demagnification of the telescope aperture is required in order to match it to this device. The technology seems to be maturing towards its application for actual systems [G. D. Love, ‘Liquid crystal adaptive optics’, in Adaptive Optics Engineering Handbook, R. K. Tyson, Ed., Marcel Dekker, 2000].
System aspects: Here we deal with deformable mirrors as a component in a system. However, some considerations apply regarding the deformable mirror as a subsystem in the adaptive optics system. This is important since the measurement and computation loads are very heavy. The deformable mirror has to be designed to relieve some of this load.
Adaptive optics systems can perform either zonal or modal correction. The first describes correction of local errors, whereas the latter describes correction of modes of either the atmosphere or the telescope. In this view it is possible to design the actuators to match specific modes [Clampin [F. Roddier, J. E. Graves, D. McKenna, and M. Northcott, ‘The University of Hawaii adaptive optics system’, SPIE Vol. 1542 248-72, 1991; M. Clampin, S. T. Durrance, D. A. Golimowski, and R. H. Barkhouser, ‘The Johns Hopkins adaptive optics coronograph’, SPIE Vol. 1542, 165-74, 1991]. The advent of fast processors and computers has simplified the systems even more. Instead of calculating specific modes and applying appropriate commands, it is possible to either break the calculation into many parallel processors, where each controls its own mode, or calculate in advance a transfer matrix between inputs and outputs to be applied in every step.
Membrane mirrors, and to a lesser extent piston mirrors, are sensitive to vibrations. The design of the mirrors should be selected so as to maximize the first resonance frequency above typical atmospheric frequencies. Otherwise it is essential to have the control and command circuits reduce the effects of these resonances.
A limiting factor in the design of deformable mirrors is their drivers or amplifiers. Most existing devices require either high voltage or high currents. Their drivers, running in parallel (one each for an actuator), a large volume and create a great amount of heat which has to be disposed off away from the telescope. Thus they have to be isolated from the telescope enclosure to avoid adding to the turbulence. This contradicts the requirement that the transmission lines from the amplifiers to the mirrors should be as short as possible. Low-power systems such as the liquid crystal and the bimorph mirror have an edge since they can be run directly out of the controller without intervening amplifiers.
There is thus a widely recognized need for, and it would be highly advantageous to have, an adaptive mirror devoid of the above limitation. In addition, there is a need for other mechanical devices which can help in maneouvering miniscule elements or devices, such as fiber optics, scanning microscope heads or memory devices reading and writing heads.